Linear Functions
y= 2x + 3, identify the slope and y-intercept.
slope = 2
Y-intercept (0,3)
What is the AOS for the equation y = -x2 - 4x ?
x = -2
The range of y = ( x + 1 )2 is..........
y is greater than and equal to 0
Factor: x2 - 7x - 18
(x-9)(x+2)
List the transformations for y = -3 ( x +1 )2
Vertex --> (-1, 0)
AofS --> h = -1
Stretched by 3
Opens down
Domain --> x is a set of all real numbers
Range --> y is less than and equal to 0
A punter kicked a football. Its path is modeled by y = -4.9x2 + 22.54x + 1.1.
What is the vertex of the football?
(2.3, 27.02)
Solve for x, 3x + 4y = 12
x = -4/3 x +4
What is the y-intercept for the function
y = 3x2 - x -11?
(0, -11 )
The range of y = -(x + 3 )2 +3 is...........
y is less than and equal to 3
Factor: 7k2 + 9k
List transformations for y = -1/2 ( x - 5 )2 -1
Vertex --> (5, -1)
AofS --> h = 5
Compressed by 1/2
Opens down
Domain --> x is a set of all real numbers
Range --> y is less than and equal to -1
A water balloon is catapulted into the air. When will it land on the ground:
y = -4.9x2 + 27x + 2.4
@ 5.6
If f(x) = x + 1 and g(x) = x2 - x + 3 find (f o g )(x)
x2 - x + 4
Which of the following is true with respect to the
functions y = x2 -5x + 10 and y = -3x2 -3x + 10 ?
A They have the same vertex
B They have the same range
C They have the same y-intercept
D All of the above
C . They have the same y-intercept
The vertex of a parabola is ( -7, -8 ) and "a" is less than 0. What is the range?
y is less than and equal to -8
Factor: 7x2 - 45x - 28
(7x + 4) (x - 7)
What is the equation of the parent function moved right 6 units, translated up 3 units and vertically
compressed by 0.91?
y = o.91( x - 6 )2 +3
A golf ball is hit and its height is given by y = -4.9x2 + 29.4x, where y is the height in metres and x is the time in seconds.
When does the ball land on the ground?
What is the maximum height the ball reaches?
lands on the ground at 6 seconds
max height = 44.1m
Write the equation that is perpendicular to 3x + 4y = 12 and passing through the point (-1, 4).
y = 4/3 x + 16/3
Which of the following functions has the narrowest
graph? y = 1/2 x2 - 2x +10
y = -1/10 x2 +20x -10
y = 1/2 x2 - 2x +10
Which value, h or k, helps to determine the range?
What is the domain of a quadratic function?
range is determined by k
domain is x is a set of all real numbers
Solve by factoring: 5p2 - p -18
p = -9/5
p = 2
Describe the transformations:
y = 2(x - 6)2 +3
Vertex --> (6, 3)
AofS --> h = 6
Stretched by 2
Opens up
Domain --> x is a set of all real numbers
Range --> y is greater than and equal to 3
Wheeley Fast Co. makes custom skateboards. Their profit is modelled by y = -2x2 + 14x - 20, where y represents their profit in hundreds of thousands of dollars and x is the number of skateboards they produce in thousands.
When do they break even (y = 0)?How many skateboards maximize their profits?
3.5 thousand skateboards (3500) maximize their profits at $4.5 hundred thousand ($450,000)
7x + 2y = 19
3x - 4y = 13
( 3, -1)
Convert y = 3( x +2 )2+ 6 to standard form
y = 3x2 +12x +18
What is the range of y = x2 - 6x + 2 ?
y is greater than and equal to -7.
Solve by factoring: 28n4 + 16n3 - 80n2
n = 0
n = 10/7
n = -2
What is the equation that results from
y = 2 ( x - 6 )2 +3 and translating it 9 units left
and 4 units down?
y = 2 ( x +3 )2 - 1
Boris throws a ball vertically upward from the top of a cliff. The path can be modelled by y = -5x2 +10x + 65, where y represents the height in metres and x represents time in seconds.
How high is the cliff?
When will the ball land on the ground?What is the maximum height that the ball reaches?
ball lands on ground @ 4.742 s
maximum height (1, 70) --> 70m